Reactions with disulphur monoxide solutions obtained by the reduction of cupric oxide by elemental sulphur

When the products of reaction between elemental sulphur and copper oxide at elevated temperature in vacuum are bubbled through chilled inert organic solvents like carbontetrachloride, orange-yellow solutions were obtained indicating the presence of lower oxide of sulphur. This lower oxide has been found to be disulphur monoxide as shown by three different types of reactions; (1) Mercury decomposition, (2) Reaction with hydrogen iodide and hydrolytic reaction in an alkaline homogeneous medium.

Compressibilities of some electrolyte solutions in relation to their stepwise dissociation

The compressibilities of some electrolytic solutions at low concentrations have been determined by employing Carstensen's phase-comparison pulse method for measuring the ultrasonic velocity differences and by simultaneously measuring their densities with a Weld-type pyknometer. The apparent molal compressibilities φ(χ̄2) of NaHSO4, KHSO 4, NaP2PO4 and Na-HPO4 have been plotted against the square root of the molarities c. The observations are explained in terms of incomplete dissociation.

The effect of viscosity and surface tension on the Taylor instability of the surface of a cavitation bubble*

This paper is devoted to a consideration of the following problem: A spherical mass of fluid of density varrho1, viscosity μ1 and external radius R is surrounded by a fluid of density varrho2 and viscosity μ2.The fluids are immiscible and incompressible. The interface is accelerated radially by g1: to study the effect of viscosity and surface tension on the stability of the interface. By analyzing the problem in spherical harmonics the mathematical problem is reduced to one of solution of the characteristic determinant equation. The particular case of a cavity bubble, where the viscosity μ1 of the fluid inside the bubble is negligible in comparison with the viscosity μ2 of the fluid outside the bubble, is considered in some detail. It is shown that viscosity has a stabilizing role on the interface; and when g1 > T(n − 1) (n + 2)/R2(varrho2 − varrho1) the stabilizing role of both viscosity and surface tension is more pronounced than would result when either of them is taken individually.

Compressibility of dilute solutions of sulphuric acid

By employing Carstensen's phase-comparison pulse method for measuring ultrasonic velocity-differences, the compressibility of sulphuric acid has been studied anew, the special interest being in the low concentration region. Sulphuric acid is found to show at first a decrease in velocity with increasing concentration and then an increase. The curve representing the apparent molal compressibility Φ(κ̄2) against the square root of the molar concentration c, shows a maximum and a minimum. This anomalous behaviour is interesting in view of the extreme anomalies in other colligative properties of sulphuric acid. A qualitative explanation of the observed maximum and minimum has been suggested.

Ultrasonic propagation through aqueous solutions of acetates

Using the pulse method in the range of 2 to 26Mc's the ultrasonic absorption, velocity and the adiabatic compressibility have been studied in eleven aqueous acetate solutions up to a concentration of 1 mole/litre. The substances studied are the acetates of lithium, sodium, potassium, ammonium, magnesium, calcium, strontium, barium, zinc, cadmium and lead. Absorption in mercuric acetate has been studied only at 2 and 6 Mc/s. Two regions of relaxation are noticed, one below 10 Mc/s and the other between 10 and 26 Mc/s. The first relaxation is ascribed to the dissociation reaction of the salt and the second one to the monomerdimer reaction of the acetic acid formed by the hydrolysis of the salt in water.

Comparison of elasticity and shell-theory solutions for finite circular cylindrical shells

A finite circular cylindrical shell subjected to a band of uniform pressure on its outer rim was investigated, using three-dimensional elasticity theory and the classical shell theories of Timoshenko (or Donnell) and Flügge. Detailed comparison of the resulting stresses and displacements was carried out for shells with ratios of inner to outer shell radii equal to 0.80, 0.85, 0.90 and 0.93 and for ratios of outer shell diameter to length of the shell equal to 0.5, 1 and 2. The ratio of band width to length of the shell was 0.2 and Poisson's ratio used was equal to 0.3. An Elliot 803 digital computer was used for numerical computations.

Approximation of solutions to fractional integral equation

In this paper we shall study a fractional integral equation in an arbitrary Banach space X. We used the analytic semigroups theory of linear operators and the fixed point method to establish the existence and uniqueness of solutions of the given problem. We also prove the existence of global solution. The existence and convergence of the Faedo–Galerkin solution to the given problem is also proved in a separable Hilbert space with some additional assumptions on the operator A. Finally we give an example to illustrate the applications of the abstract results.

NMR relaxation study of disorder in condensed matter: solid solutions of betaine phosphate and phosphite

Proton NMR relaxation measurements have been carried out in anti-ferroelectric Betaine phosphate (BP), ferroelectric Betaine phosphite (BPI) and the mixed system BPI(1-x)BPx, at 11.4MHz and 23.3MHz from 300K to 80K for x=0.0, 0.25, 0.45, 0.85, and 1.0. The temperature dependence of spin lattice relaxation time T, exhibits two minima as expected from the BPP model in BP and BPI. The Larmor frequency dependence of T, in the mixed system is rather unusual and exhibits different slopes for the low temperature wings at the two frequencies, which is a clear experimental evidence of the presence of different methyl groups with different activation energies (E-a) indicating disorder.

Effect of viscosity stratification on secondary and nonmodal instabilities

The effect of viscosity stratification on the different mechanism of transition to turbulence is not well understood. In this paper, a viscosity variation normal to the flow in a channel is investigated. The primary and secondary instability are computed, and the transient growth is analysed. It is found that viscosity stratification can have different effects in each case.

Stability and transition in the flow of polymer solutions

The linear stability analysis of a plane Couette flow of viscoelastic fluid have been studied with the emphasis on two dimensional disturbances with wave number k similar to Re-1/2, where Re is Reynolds number based on maximum velocity and channel width. We employ three models to represent the dilute polymer solution: the classical Oldroyd-B model, the Oldroyd-B model with artificial diffusivity and the non-homogeneous polymer model. The result of the linear stability analysis is found to be sensitive to the polymer model used. While the plane Couette flow is found to be stable to infinitesimal disturbances for the first two models, the last one exhibits a linear instability.

A simple technique for approximate solutions of the Falkner-Skan equation

A simple, sufficiently accurate and efficient method for approximate solutions of the Falkner-Skan equation is proposed here for a wide range of the pressure gradient parameter. The proposed approximate solutions are obtained utilising a known solution of another differential equation.